This invention relates to digital filtering of data modulated electrical signals in modems.
Digital filters, wherein the signal value is sampled at a high rate and the resultant samples are arithmetically processed to yield a filter output, are often used to fulfill the various modem filtering requirements. This is particularly true of transversal digital filters where a predetermined number of the most recent samples are stored, e.g., as in a delay line which defines the time span of the filter. Following the taking of each new sample and its entry into the delay line, each of the samples currently stored is multiplied by a tap coefficient, there being one tap coefficient associated with each unit of the delay line. The sum of all such multiplications yields the filter output.
A linear phase digital filter posesses the property that the values of its tap coefficients are symmetrical about the center of its time span. In A. V. Oppenheim and R. W. Schafer, Digital Signal Processing, Prentice-Hall (1975), pp. 157-60, is shown a method of using this symmetry to reduce the number of multiplications required in a digital filter which uses a tapped delay line for sample storage.